An increase in NA (high numerical aperture) of exposure apparatus using ArF exposure light of 193 nm wavelength is in progress to deal with the miniaturization of semiconductor devices. A further increase in NA has been made as a result of the introduction of a liquid immersion exposure technique, presently leading to the practical application of NA 1.35.
To deal with such demands for miniaturization and increases in NA, higher flatness of a transfer mask is expected. When the flatness of a mask surface as an object point is reduced, focused position of an image point on a wafer transferred through a projection lens fluctuates. Therefore, reduction in the mask surface flatness causes a decrease in allowable focus latitude. On the other hand, due to the optical principle, an increase in NA of a projection lens reduces focal depth. Therefore, as increases in NA continue, focus latitude in the lithography process decreases, so that there is a demand for high flatness on the mask surface. For this reason, on a transparent substrate used for a mask blank which is an original plate for manufacturing a transfer mask, there is a demand for high flatness on a principal surface to which a thin film is provided for forming a pattern. To deal with the demand for flatness, double-sided polishing for polishing both front and rear faces of a mask blank substrate using a polishing pad such as a polishing fabric and a polishing liquid containing abrasive grains has frequently been used as disclosed in Patent Document 1, for example. However, there is a limitation in increasing flatness of the principal surface of the transparent substrate in its polishing using conventional double side polishing apparatus. Therefore, a technique has been developed in which a shape of a principal surface of a substrate is measured and relatively convex portions are subjected to plasma etching to achieve flatness, as described in Patent Document 2.
Further, there is a problem that the influence of the lens aberration of the projection optical system on transfer accuracy is becoming greater due to a decrease in focus latitude in the lithography process together with an increase in NA of exposure apparatus. To solve this problem, Patent Document 3 discloses two correction optical elements having a surface shape that can be defined by a Zernike polynomial for correcting aberration caused by lens heating effects of a projection optical system.